论文标题

车辆路线问题的当地路线

Local Area Routes for Vehicle Routing Problems

论文作者

Mandal, Udayan, Regan, Amelia, Yarkony, Julian

论文摘要

我们考虑了提高柱产生效率(CG)方法来解决车辆路线问题的方法。我们在CG公式中引入了局部区域(LA)路线松弛,这是常用的NG-Route松弛度和降低状态空间松弛(DSSR)的替代/补充。 LA路线是NG路由的子集和基本路线的超级集合。通常,CG的定价阶段必须产生基本路线,这些路线是没有重复客户的路线,使用可能在计算上昂贵的过程。非元素路线至少访问至少一个客户,创建一个周期。 LA路线放宽了以允许有效定价的方式成为基本途径的约束。从NG-Route放松方面,最好理解LA路线。 NG路由是允许在空间中具有非定位循环的路线。这意味着,在周期中,至少有一个中间客户(称为断路器)必须考虑到周期中的启动客户在空间上远离。使用一组与路线末端的路线上的客户相对应的特殊索引来描述LA路线。 LA路线的松弛进一步限制了一组允许的周期,超出了NG路由的循环,并强化断路器必须位于特殊索引位于特殊索引,其中一组特殊索引被递归地定义为如下。该路线中的第一个特殊索引是索引1,这意味着它与路线中的第一个客户相关联。 K'th特殊索引对应于K-1第三个特殊索引之后的第一个客户,该索引并不是(在空间上远离)位于K-1'特殊索引的客户的邻居。我们证明,与标准DSSR相比,LA路线松弛可以显着提高定价的计算速度。

We consider an approach for improving the efficiency of column generation (CG) methods for solving vehicle routing problems. We introduce Local Area (LA) route relaxations, an alternative/complement to the commonly used ng-route relaxations and Decremental State Space Relaxations (DSSR) inside of CG formulations. LA routes are a subset of ng-routes and a super-set of elementary routes. Normally, the pricing stage of CG must produce elementary routes, which are routes without repeated customers, using processes which can be computationally expensive. Non-elementary routes visit at least one customer more than once, creating a cycle. LA routes relax the constraint of being an elementary route in such a manner as to permit efficient pricing. LA routes are best understood in terms of ng-route relaxations. Ng-routes are routes which are permitted to have non-localized cycles in space; this means that at least one intermediate customer (called a breaker) in the cycle must consider the starting customer in the cycle to be spatially far away. LA routes are described using a set of special indexes corresponding to customers on the route ordered from the start to the end of the route. LA route relaxations further restrict the set of permitted cycles beyond that of ng-routes by additionally enforcing that the breaker must be a located at a special index where the set of special indexes is defined recursively as follows. The first special index in the route is at index 1 meaning that it is associated with the first customer in the route. The k'th special index corresponds to the first customer after the k-1'th special index, that is not considered to be a neighbor of (considered spatially far from) the customer located at the k-1'th special index. We demonstrate that LA route relaxations can significantly improve the computational speed of pricing when compared to the standard DSSR.

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